Currying

From HaskellWiki

Currying is the process of transforming a function that takes multiple arguments into a function that takes just a single argument and returns another function if any arguments are still needed. In Haskell, all functions are considered curried: that is, all functions in Haskell take just single arguments.

This is mostly hidden in notation, and so may not be apparent to a new Haskeller. Let's take the function

div::Int->Int->Int

which performs integer division. The expression

div112

unsurprisingly evaluates to

5

.
But there's more that's going on than immediately meets the untrained eye. It's a two-part process. First,

div11

is evaluated and returns a function of type

Int->Int

Then that resulting function is applied to the value

2

, and yields

5

.

You'll notice that the notation for types reflects this: you can read

Int->Int->Int

incorrectly as "takes two

Int

s and returns an

Int

", but what it's really saying is "takes an

Int

and returns something of the type

Int->Int

--that is, it returns a function that takes an

Int

and returns an

Int

. (One can write the type as

Int x Int->Int

if you really mean the former--but since all functions in Haskell are curried, that's not legal Haskell. Alternatively, using tuples, you can write

(Int,Int)->Int

, but keep in mind that the tuple constructor

(,)

itself can be curried.)

Much of the time, currying can be ignored by the new programmer. The major advantage of considering all functions as curried is theoretical: formal proofs are easier when all functions are treated uniformly (one argument in, one result out). Having said that, there are Haskell idioms and techniques for which you need to understand currying.

Currying provides a convenient way of writing some functions without having to explicitly name them:

(1+)

(unsugared:

(+)1

) is the "increment" function,

(2*)

is the "double" function,

("\t"++)

is the "indent" function,

(`elem` "AEIOU")

is the "is-capital-vowel-in-English" function (ignoring the "sometimes Y").